Royal Bank of Scotland (RBS) has hired headhunters to take on one of the toughest boardroom searches in Britain - recruiting the next chairman of the taxpayer-backed lender.

Sky News has learnt that directors of RBS have appointed Egon Zehnder International to assist with identifying a successor to Sir Philip Hampton, who will step down in 2015 after more than six years in the role.

Egon Zehnder was appointed recently and is in the process of approaching potential candidates for the job, according to people close to the situation.

The search is being led by Sir Sandy Crombie, the former Standard Life boss who is RBS's senior independent director, but will also have substantial input from the Treasury and UK Financial Investments (UKFI), which manages the Government's stake in the bank.

The exact timing of Sir Philip's departure will depend on the availability of his successor, although he is likely to remain in place until after next May's general election since the new chairman will want to know the identity of the next Government.

RBS remains almost 80% state-owned more than five years after its £45.5bn rescue by UK taxpayers and there is little prospect of the entire shareholding being returned to the private sector for many years.

For much of its time in state ownership, the bank has been a political football, having been forced into lending targets and sharper reductions to bonus pools than its private sector rivals.

Sir Philip was ordered by George Osborne to sack Stephen Hester, RBS's former chief executive, last year amid dissatisfaction at the Treasury at the pace of the bank's reconstruction.

It has since decided to focus more closely on its personal banking and small business operations in the UK, with Ross McEwan, Mr Hester's successor, vowing to improve the way it treats customers.

Other fines levied by regulators since its bail-out include penalties of hundreds of millions of pounds for manipulating benchmark rates and poor treatment of customers of Coutts, its wealth management business.

The bank's new chairman is likely to have a full in-tray as they attempt to steer it back towards full private sector ownership.

There have been some signs of improvement, with RBS announcing its half-year results a week early because they were better than forecast.